What is the radius of a a circle that touches the parabola 1/2x² at (2,2) and the x-axis?

Here the derivative of our parabola is 2
And if we getWhat is v?

This could give us the common point between those two circles; that would be the center of the circle that we want. Which two circles?
But this gives me a strange equation, that I really don't know what it is for. Why is it strange?

v is the x coordinate of the place where the circle touches the x-axis. The Xo in your graph.
I read somewhere that you could get get center of the circle by using two circles in the places where we have points, the parabola and the x-axis.
Using this formula I'll get a equation with some unwanted X's and Y's and V's, so it's probably not the best idea to use it.

I really thought about using a perpendicular here. But what is the easiest way to get it?

I would use it like f(x-2)+2 using the translation principles.

So

But what about the tangent line?

To get it you used right?
I was kind of confused in that terms too, since I hadn't seen calculus in some time.

You have two equations on x0, y0: the first says that the distance from (x0,y0) to (2,2) equals the distance from (x0,y0) to (x0,0), and the second says that (x0,y0) lies on the graph of y = 3 - x/2.

Hi emakarov!
I've managed to do it!!!
Yes, it was quite easy with your explanation! Thank you so much!
There's another way that I don't understand well

What's that -1 and that 2?
I'm not sure, but the b^2-5b+5 could be acquired in some way, replacing a for b in the first equation.
This way it was answered in terms of y, it seems easier to use x though!